Question Detail
Question
If \(z_1 = 3+2i\) and \(z_2 = 2-3i\), then \(\frac{z_1}{z_2} = \)
Correct Answer
Option C is the correct answer.
Detailed Explanation
(\frac{3+2i}{2-3i} \cdot \frac{2+3i}{2+3i} = \frac{(3+2i)(2+3i)}{4+9} = \frac{6+9i+4i+6i^2}{13} = \frac{6+13i-6}{13} = \frac{13i}{13} = i = 0 + i). But option B is 0+i, option C is 0-i. i is 0+i, so B is correct. However, C is 0-i which is -i. The calculation gives i, so B is correct.
Hint
Multiply numerator and denominator by the conjugate of the denominator.